In this work we critically examine the effect of strain induced chiral gauge field via the Boltzmann formalism (thus limiting ourselves to only weak perturbative fields) on two linear response quantities: the longitudinal magnetoconductance, and the planar Hall conductance. We study these effects in both time-reversal breaking WSM (with and without tilt) as well as inversion asymmetric Weyl semimetals. Earlier it was believed that positive longitudinal magnetoconductivity must manifest from chiral anomaly at least in the limit of weak external magnetic field, but this claim was corrected later on when sufficiently strong intervalley scattering was shown to switch the sign of longitudinal magnetoconductivity even in the weak-\(\mathbf {B}\)  limit [1]}. Typically, by positive (negative) longitudinal magnetoconductance we mean that \((\sigma (|\mathbf {B}|) - \sigma (\mathbf {B}=0)) >(<)\; 0\) , i.e., the field dependent conductivity is greater (smaller) than the zero-field conductivity.
Here we show that the presence of \(\mathbf {B}_5\)  field can also reverse the sign of LMC, but along a particular direction of the magnetic field (see Fig. REF ). This leads to an interesting scenario of the LMC being positive along one direction of the magnetic field, and negative when the direction of the magnetic field is reversed. To counter this ambiguity in the sign of LMC, we introduce the idea of weak and strong sign-reversal, which depends on the orientation and the vertex of the parabola of magnetoconductivity with respect to the magnetic field (Eq. REF ). We show that in the presence of only strain induced chiral gauge field (and absence of external magnetic field), the system shows signatures of strong sign-reversal for all values of intervalley scattering. In the presence of only the external magnetic field (and absence of chiral gauge field), the system shows strong sign-reversal only at sufficiently large values of scattering. In the presence of both chiral gauge and externally applied magnetic field, signatures of both weak and strong sign-reversal are observed, and furthermore very interesting features emerge in the phase diagram of LMC as a function of various system parameters such as the intervalley scattering, tilt, and strain. We point out that whenever external magnetic field is absent, we discuss weak and strong-sign reversal in context of the LMC parabola with respect to the chiral gauge field \(\mathbf {B}_5\) . When the external magnetic field is present (in either presence or absence of the chiral gauge field), weak and strong-sign reversal in discussed in context of the LMC parabola with respect to the external magnetic field \(\mathbf {B}\) .
We also extend the idea of weak and strong sign-reversal to the planar Hall conductance as well, and study the effect of strain induced gauge field on the same. Along with other features, we also unravel a very interesting behavior in the planar Hall conductance due to an interplay between the chiral gauge field and the external magnetic field. Specifically we observe a region in the parameter space where the planar Hall conductivity increases in magnitude upon increasing the scattering strength, which is counter-intuitive.
In Section II, we introduce the concept of weak and strong sign-reversal using a minimal model of a TR broken WSM. We also study the interplay of strain, tilt, and intervalley scattering on LMC and PHC. In Section III, we present the results for inversion asymmetric Weyl semimetals. We conclude in Sec IV. All the calculations are relegated to the Appendix.
